Modelling Stochastic Star Formation History of Dwarf Galaxies in GRUMPY

We investigate the impact of bursty star formation on several galaxy scaling relations of dwarf galaxies using the $\texttt{GRUMPY}$ galaxy formation model. While this model reproduces the star formation rate (SFR)-stellar mass, stellar mass-gas mass, and stellar mass-metallicity relations, the scatter of these relations in the original model is smaller than observed. We explore the effects of additional stochasticity of SFR on the scaling relations using a model that reproduces the level of SFR burstiness in high-resolution zoom-in simulations. The additional SFR stochasticity increases the scatter in the SFR-stellar mass relation to a level similar to that exhibited by most nearby dwarf galaxies. The most extreme observed starbursting dwarfs, however, require higher levels of SFR stochasticity. We find that bursty star formation increases the scatter in the colour-magnitude distribution (CMD) for brighter dwarf galaxies $(M_V < -12)$ to the observed level, but not for fainter ones for which scatter remains significantly smaller than observed. This is due to the predominant old stellar populations in these faint model galaxies and their generally declining SFR over the past 10 Gyrs, rather than quenching caused by reionization. We examine the possibility that the colour scatter is due to scatter in metallicity, but show that the level of scatter required leads to an overestimation of scatter in the metallicity-mass relation. This illustrates that the scatter of observed scaling relations in the dwarf galaxy regime represents a powerful constraint on the properties of their star formation.